EDIT: i just noticed the topic was about bass trombone. what have you been playing before? how high of notes are we talking about? if you're playing bass trombone a double trigger is definitely better than a single but if you have been playing a tenor than i would suggest sticking to it.
embouchure
haha i have never heard anyone besides instructors and first year students use this word before
anyway,
1. When hitting low peddle notes (Bb, A... etc.) I tend to change my embouchure so I can the notes feel more full and give a nice crash to them, is this normal? is there another method that would be usuable?
when changing any notes, you're changing your mouth i don't know what you're trying to say here, but yeah it's normal. if it gives you the sound you want and it doesn't strain your lips, then there's no problem.
also pedal tones do you mean while pulling the bass pedal or playing below scale? there are lots of Bbs and As
2. Are there any breathing exercises that are effective for being able to hold and sustain peddle notes at the appropriate sounds level?
just your standard breathing procedures here, sorry. but generally pedal tones take less air to push out a nice sound than the really high notes, so if you can sustain really high notes you should be able to sustain pedal tones.
3. How much of a difference is there between an F attachment trigger trombone and a double trigger trombone?
the double trigger trombone is the bass, right? the f trigger will just lower your sound five half steps, and i think the bass lowers it twelve but don't quote me on that. THAT SAID if you want to keep hitting high notes i would suggest NOT using a bass trombone, because it's larger bore harder to hit the high notes. not impossible but it will take more. Also, you mentioned mostly doing jazz and i would like to point out that a regular pea shooter is the best for this sound. the f attachment and bass trombones have cleaner, prettier sounds that lend themselves really well to concert and orchestra, but for a fuller, jazzier sound it's often better to use the old fashioned one.
4. With soloing and improv, is it recomended to stay in the high range of the trombone or should I be playful and use the entire range? (I'm asking this because I've done improv and used the entire range, the only problem is that it's very hard to make a clean sound with a large range.
just like any instrument, this depends on the song. some songs you will want to stay higher, some you'll want to stay lower, some you'll want to use your full range.